Make it a tiny % of net worth, with a modest minimum and watch EVERYONE obey. Or at least something meaningful to everyone, or don't make it a fine. Use some other carrot or stick.
One thing about daycares is that you will essentially never find "someone who's barely making ends meet" and "a billionaire" with kids at the same daycare, so a surcharge for out-of-normal-expectations service does not need to be designed to address both cases.
(In fact, you'll probably not find a billionaire with kids at any daycare, their hired childcare workers won't be shared with other people, and will probably be adequately compensated up front in a way which anticipates a fair degree of schedule variability.)
OTOH, with red light cameras, you also don't need to scale the fine to work with both, because the entire purpose is to bind the lower classes while exempting the upper from any substantial burden. (The least cynical explanation is that it is to discourage behavior which might incur liability grossly exceeding the mandatory level of insurance company by those least able to cover the cost of that liability, thereby avoiding uncompensated harms, but the realistic explanation is...not so generous.)
I grew up with the children of a multi-billionaire. His kids went to the same daycare as I did, and it wasn’t particularly fancy.
Some ultra-wealthy people live fairly normal-looking lives.
Steve Jobs's kids drew on an eMac with markers or something. He made them make an appoint for the store's Genius Bar and wait in line to have it looked at like everyone else. I don't know anything about how the staff tried to clean it or the outcome.
I lack the context and knowledge to understand how this would work, but I am curious (enough to ask but not enough to google it, admittedly).
Enlightenment and utopia across that simple bridge